Objectives:Several approaches including transformation, generalized linear mixed models (GLMM), and semi-parametric two part models are used to account for heteroscedasticity, skewness, and zeros in healthcare cost analysis. Analyzing aggregated total cost from separate service sources is another critical problem. Analyzing aggregated cost could hide factors that have a differential impact on cost sources and lead to incorrect conclusions due to failure to account for the shared correlation among cost variables. Therefore, we propose a multivariate GLMM (mGLMM) approach that addresses this problem.

Methods:mGLMM jointly models multiple cost outcomes (e.g., inpatient, outpatient, and pharmacy) with a common random intercept to account for correlation among the outcomes. The joint modeling approach allows assessment of differential covariates effects on each cost type accounting for shared correlation across cost variables and relevant covariates. We compare log-normal, gamma, and exponential distributions to assess whether the proposed joint modeling is robust to distributional assumptions. Goodness of fit measures scaled to sample size, residual by predicted plot, and standard error of estimated parameter are used for model comparison. We use data from a national cohort of 892,223 Veterans with diabetes (followed 2002-2006).

Results:Log-normal models showed better fit in terms of AIC in both mGLMM (17.6, 112.0, 112.0 for log-normal, gamma, and exponential respectively) and GLMM (1.29, 8.83, 8.84) models. The residual by predicted plot for log-normal also exhibited better control of heteroscedasticity. These features of the log-normal distribution were more pronounced in the joint model than the independent models. Joint modeling estimates of healthcare cost differences by covariates were also more realistic and in the expected direction than those from independent models. The relative outpatient cost of those with medication possession ratio (MPR) above 80% was 1.13 times higher than those with MPR <80% in the independent models whereas it was 0.67 times lower in the joint model.

Implications:Cost analysis studies should allow for shared correlation across cost variables by using the proposed joint modeling approach when examining differences in healthcare cost by covariates.

Impacts:Ignoring correlation among multivariate outcomes could lead to erroneous conclusions as well as biased estimates of cost projections.